Calculating Compound Interest and Simple Interest: A Comprehensive Guide

Understanding the principles of compound interest and simple interest is crucial for managing finances and investments effectively. In this article, we will explore a detailed example of calculating compound interest for a certain sum over two years at 10% per annum, and subsequently, determine the simple interest for double the time with half the rate. By the end of this article, you will have a clear understanding of how to solve similar problems.

1. What is Compound Interest?

Compound interest is the interest calculated on the initial principal and the accumulated interest from previous periods. The formula for compound interest is:

CI P × (1 frac{r}{100})^t - P)

Where:

P is the principal amount r is the annual interest rate in percentage t is the time the money is invested for, in years

2. Calculating the Principal Amount Using Compound Interest

In the given problem, we have the compound interest (CI) of Rs. 210 for a period of 2 years at a rate of 10% per annum. We need to find the principal amount (P).

Apply the compound interest formula:

210 P × (1 frac{10}{100})^2 - P

210 P × 1.21 - P

210 0.21P

P frac{210}{0.21} Rs. 1000

The sum (P) is Rs. 1000.

3. Calculating the Simple Interest

Now, we need to calculate the simple interest (SI) for a period of 4 years at 5% per annum. The formula for simple interest is:

SI frac{P × r × n}{100}

Where:

P 1000 r 5 n 4

Substitute the values in the formula:

SI frac{1000 × 5 × 4}{100}

SI frac{20000}{100}

SI Rs. 200

The simple interest for double the time at half the rate is Rs. 200.

4. Summary

By following the above steps, we have calculated the principal amount using the compound interest formula and determined the simple interest for double the time with half the rate. Here are the key findings:

Conclusion

Understanding the principles of compound interest and simple interest helps in making informed financial decisions. This article provided a step-by-step guide to solve a problem related to compound interest and simple interest, demonstrating the practical application of these concepts.